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. 2016 Jul 21;6:30098. doi: 10.1038/srep30098

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between node 1 and node 2. Nodes 1 and 2 can be introduced by their common neighbors 3 and 4. (a) Node 3 introduces his friends to node 1. Only neighbor nodes 2, 5, 7 can be introduced to node 1 but excludes node 4, since node 4 has been a friend of node 1. Thus, the probability of node 3 introducing node 2 to node 1 is: f₂₃₁ = 1/3; (b) node 2 is introduced to node 1 by node 4, here only nodes 2 and 6 can be introduced to node 1. As a result, the probability f₂₄₁ = 1/2; (c) node 1 is introduced to node 2 by node 3, here only nodes 1 and 5 can be introduced to node 1. As a result, the probability f₁₃₂ = 1/2; (d) node 1 is introduced to node 2 by node 4, here only nodes 1 and 6 can be introduced to node 1. As a result, the probability f₁₄₂ = 1/2. We have f₂₁ = 1/3 + 1/2 by combing (a,b), and f₁₂ = 1/2 + 1/2 by combing (c,d). So the FR similarity index is .

Inline graphic — between node 1 and node 2. Nodes 1 and 2 can be introduced by their common neighbors 3 and 4. (a) Node 3 introduces his friends to node 1. Only neighbor nodes 2, 5, 7 can be introduced to node 1 but excludes node 4, since node 4 has been a friend of node 1. Thus, the probability of node 3 introducing node 2 to node 1 is: f₂₃₁ = 1/3; (b) node 2 is introduced to node 1 by node 4, here only nodes 2 and 6 can be introduced to node 1. As a result, the probability f₂₄₁ = 1/2; (c) node 1 is introduced to node 2 by node 3, here only nodes 1 and 5 can be introduced to node 1. As a result, the probability f₁₃₂ = 1/2; (d) node 1 is introduced to node 2 by node 4, here only nodes 1 and 6 can be introduced to node 1. As a result, the probability f₁₄₂ = 1/2. We have f₂₁ = 1/3 + 1/2 by combing (a,b), and f₁₂ = 1/2 + 1/2 by combing (c,d). So the FR similarity index is .